The study of LFs in FGs was mainly focused on individual FGs, due to their paucity. As a consequence, most of the first results were contradictory. [1]} found, for the FG called RX J1552.2+2013, M\(^*=-21.18\pm 0.57\)  and \(\alpha = -0.77\pm 0.37\)  using spectroscopically-confirmed members, or M\(^*=-21.27\pm 0.62\)  and \(\alpha = -0.64\pm 0.30\)  for photometrically-selected galaxies in the \(r-\) band. In the same year, [2]} computed \(M^*=-20.40\pm 0.22\)  and \(\alpha = -1.23\pm 0.28\)  for RX J1416.4+2315, a fossil system with a mass similar to RX J1552.2+2013. Also [3]} presented an LF for a single FG (NGC 1407), finding \(\alpha = -1.35\) .
The difference, especially in the faint-end slope, is important. In fact, \(\alpha = - 1\)  indicates a flat LF, in which the number of dwarf galaxies is not changing with magnitude. On the other hand, in a steeper function like that of [2]}, the number of dwarf galaxies is rapidely growing and, in a flatter one like that of [1]} it is decreasing.
